“The current situation in Shajaiye today is tragic,” said Ahmed Sidu, a photographer, who went back to his home as soon as he heard that Israeli forces had pulled out.

“There was only misery on people’s faces,” he added, referring to others who returned and found “no shelter and no water.”

Palestinian Civil Defense emergency services agency said in a statement on Thursday night that their emergency and rescue crews had recovered more than 60 bodies from Shajaiye after the Israeli military withdrawal.

The statement added that dozens of people remain missing and were feared to be buried under the rubble. The raid had destroyed most of the buildings and homes that were left standing after Israel’s initial invasion in October, it said. The death toll could not be independently confirmed.

“The Shajaiye area has become an uninhabitable area, lacking all necessities of life,” the organization said in a statement.

The Israeli military reported this week that it had concluded its operation in Shajaiye, though on Friday said it did not confirm that its troops had pulled out of the neighborhood.

The military had announced the operation in Shajaiye more than two weeks ago, along with evacuation orders that the U.N. office of humanitarian affairs said had pushed 60,000 to 80,000 people from areas east and northeast of Gaza City. It later expanded its ground operations and issued warnings to evacuate to other parts of the city.

On Friday, the military said that among the fighters killed in the operation was the deputy commander of Hamas’s Shajaiye Battalion, Ayman Showadeh. Israeli officials said Mr. Showadeh was previously “a key operative” at Hamas’s operation headquarters and was involved in directing the Oct. 7 Hamas-led attack that set off the war in Gaza.

Karam Hassan, a Gaza City resident who went to Shajaiye to see the aftermath of the raid, said that families who had hoped to return to their residences found themselves having to stay in shelters and displacement centers because nothing was left of their homes.

“Homes are all reduced to piles of rubble, bakeries, and shops are destroyed and even the streets have been dug up,” Mr. Hassan said. “The situation is very tough and the scale of destruction is immense.”

Mr. Sidu, the photographer, said he was among the few whose home, on the outskirts of Shajaiye, had suffered little damage, but he added he was still not sure he could stay there because all of the infrastructure had been destroyed. “How do we live without basic necessities and without water?” he said.

“There may be a relative calm now in terms of aircraft and artillery shelling,” Mr. Sidu said. “But residents were now facing “a severe shortage of potable water, internet and communications networks and were suffering emotionally.”

He said that some people whose buildings and houses were destroyed had set up tents near the rubble and were determined to stay and “create a kind of familiarity and neighborhood atmosphere that binds them together.”

Israeli forces have returned to clear out Hamas fighters in several parts of Gaza that they had previously secured, especially in the north, as Hamas has regrouped amid the anarchy of the nine-month war.

This week, the Israeli military was operating in other parts of Gaza City, including the Tal al-Hawa neighborhood, where Israeli forces stormed a vacated United Nations compound, and the southern outskirts of the upscale Al-Rimal neighborhood.

Palestinian Civil Defense said on Friday that their crews began recovering bodies from Tal Al-Hawa and the Al-Sinaa neighborhoods, as they said the Israeli forces appeared to be leaving those areas as well. At least 60 corpses had been recovered, the organization said.

The Israeli military did not confirm its forces were also pulling out of those areas.

The military in a statement that Israeli forces had raided “a Hamas combat complex embedded inside a compound previously used by UNRWA,” the main United Nations agency that assists Palestinians in the area. Troops were “engaged in close-quarters combat” with militants who had “fortified themselves inside,” the statement said.

A spokeswoman for UNRWA, Juliette Touma, confirmed that the facility had been evacuated in October when the war started and that the agency had “no way to verify” the Israeli claims. The agency has “repeatedly called for independent investigations and queries into these allegations and any violation of international humanitarian law,” she said.

Rawan Sheikh Ahmad contributed reporting.

Later on Thursday, President Biden also expressed guarded optimism about the direction of negotiations during a news conference closing a NATO conference in Washington, D.C. “There’s still gaps to close, but we’re making progress,” the president said. “The trend is positive. I’m determined to get this deal done and bring an end to this war which should end now.”

Earlier this week, the Mr. Biden dispatched his top aide for Middle East affairs, Brett McGurk, to Israel for discussions with the government there, while William J. Burns, the C.I.A. director, traveled to Doha, Qatar, for talks with the Egyptian, Qatari and Israeli officials negotiating over the release of the hostages.

On Friday, Mr. McGurk led the American delegation for further talks in Cairo on the framework of a three-phase deal that is backed by the United States and the United Nations. After holding meetings with the Israeli negotiating team on Thursday, Mr. Netanyahu dispatched a delegation led by the head of Israel’s Shin Bet intelligence service to Cairo for continued discussions.

Negotiators have tried to overcome hurdles to a deal by reaching precise agreements on the exchanges of Palestinian prisoners for Israeli hostages in its first phase. At the same time they have pushed for agreement on the broader framework for subsequent phases of the deal.

The framework discussions include the two most contentious issues: whether Israel will agree to end the war, withdraw from Gaza and respect a permanent cease-fire; and whether Hamas will agree to give up control of the Gaza Strip, according to a person briefed on the negotiations.

Both Israel and Hamas remain exceptionally wary about whether the other side is truly ready to make concessions.

Husam Badran, a senior Hamas official, said his group had shown “great flexibility” in discussions with mediators, especially in making language changes, but had held firm to its demand that Israel agree to a permanent cease-fire.

“We’re not obstinate and rigid in negotiating,” he said in an interview in Doha. “If there are some phrases that will make the negotiations easier and lead to the same result — the end of the war — we have no problem.”

Palestinians have grown weary of the war, which has killed tens of thousands of people in Gaza. While most still blame Israel for the death and destruction, anger at Hamas — and a willingness to express that resentment — is growing.

Created in 1949 after the first Arab-Israel war, the agency provides schools, health clinic, social services and aid to millions of Palestinian refugees and their descendants in the Gaza Strip, the West Bank, Jordan, Syria and Lebanon.

Israel’s right-wing government, led by Prime Minister Benjamin Netanyahu, has called for the agency to be dismantled, accusing it of being complicit with Hamas, the armed group that controlled the Gaza Strip and is now at war with Israel.

More than a dozen donor countries had halted funding to the agency in January after Israel accused 12 of its employees of being involved in the Oct. 7 terrorist attacks last year. Israel later alleged that one in 10 of the agency’s 13,000 employees in Gaza was a member of Hamas or its ally, Palestinian Islamic Jihad.

The United Nations is conducting an internal investigation into the allegations, and most donors, including the United States, have since resumed providing financing.

The 118 states who pledged to support UNRWA included all the members of the powerful Security Council. The group issued a joint statement saying “that UNRWA is the backbone of all humanitarian response in Gaza, and recognizing that no organization can replace or substitute UNRWA’s capacity.”

Addressing the conference on Friday, the head of the agency, Philippe Lazzarini, said his agency had “paid a terrible price” during the war, noting that 195 staff members had been killed during the war. In addition, at least 190 of its operations, including schools to clinics, have been damaged or destroyed. He said his agency was committed to remaining neutral in the conflict between Palestinians and Israel.

Mr. Lazzarini said the show of solidarity and support of the member states came “at a critical time as UNRWA undergoes unprecedented attacks and systematic attempts to dismantle it.”

One reason to be careful, those researchers said, is that any estimate of excess deaths would rely on data from Gaza’s health sector, which has been devastated by the conflict. Another reason, they said, is that it is hard to predict how epidemics and hunger, two threats to human life that can be triggered by war, will evolve. And Israel has not permitted researchers to enter the enclave since the start of the war last October.

The letter in The Lancet, which said that counting indirect deaths in Gaza was “difficult but essential,” based its estimate on looking at previous studies of recent conflicts, which indicated that three to 15 times as many people died indirectly for every person who had died violently. Applying what they called a “conservative estimate of four indirect deaths per one direct death,” the authors wrote that it was “not implausible” to estimate that about 186,000 deaths could eventually be attributable to the conflict in Gaza.

The letter, which The Lancet said had not been peer-reviewed, as is the case with other letters it publishes, provoked a significant response. The Board of Deputies of British Jews, which represents the Jewish community in Britain, said that the estimate was “little more than conjecture.”

Col. Elad Goren, an official with COGAT, the arm of the Israeli military that implements policy in Gaza, sidestepped a question about excess deaths.

Salim Yusuf, a cardiologist and epidemiologist in Canada who co-wrote the letter, said in an email that the estimate was based on studies of past conflicts and acknowledged that, “inevitably, these are projections.” “The point is that the real numbers of dead will be very large,” he said.

Michael Spagat, a professor of economics at Royal Holloway College at the University of London, who has written about the toll of the war in Gaza, wrote in an analysis that the letter “lacks a solid foundation and is implausible.” He argued that the authors had compared Gaza with a small and unrepresentative sample of other conflicts, and that conditions in Gaza, a small territory under intense international attention, are unique.

In an interview, Mr. Spagat cited other reasons to be cautious when discussing excess deaths in Gaza. He said that fears of major outbreaks of infectious diseases such as cholera have yet to materialize and that, although humanitarian agencies are warning of catastrophic levels of hunger, there is little evidence of widespread deaths because of starvation.

Still, Mr. Spagat said that it was “fair to call attention to the fact that not all of the deaths are going to be direct violent ones.”

The letter in The Lancet is not the first effort to quantify the human toll in Gaza beyond the figures reported by Gazan health authorities.

In February, epidemiologists at Johns Hopkins University and the London School of Hygiene and Tropical Medicine produced a model showing three different war scenarios affecting overall deaths in Gaza. They projected that if fighting and humanitarian access remained at the same levels, there could be an additional 58,260 deaths in the six months from March through August. Around 9,000 deaths have been directly attributed to the war since then by Gaza’s health ministry.

The health ministry says that more than 38,000 people have died in Gaza since Oct. 7, when Hamas, which controls the territory, led an attack on Israel in which 1,200 people were killed. While the ministry’s tally is broadly accepted, there remain questions about its methodologies and record keeping, as well as contradictions between its statements and underlying data. Most civilian victims, the ministry says, are women and children. But the figures do not distinguish between civilians and combatants.

The subject of excess deaths is sensitive because it touches on the collateral cost of Israel’s war against Hamas. On top of the large death toll, the attacks have damaged hospitals and shelters. Aid officials say that Israel has also restricted access to the fuel that medical facilities need to operate. Israeli officials say they do all they can to spare civilians, but blame Hamas for placing its forces in urban centers and civilian facilities. They have also said that aid agencies’ logistical difficulties, rather than Israeli restrictions, are to blame for the limited amount of humanitarian aid that is getting to Gazans.

Before the war, Gaza’s health sector produced reliable data, which helps in modeling excess deaths, but lack of access to Gaza for researchers makes the task more difficult, according to Zeina Jamaluddine, an epidemiologist at the London School of Hygiene and Tropical Medicine.

Gabby Sobelman contributed reporting.